06 Cap 5 - interharmonics-and-flicker-2015.pdf

CHAPTER 5
INTERHARMONICS AND FLICKER
5.1 INTERHARMONICS
IEC [1] defines interharmonics as “Between the harmonics of the power frequency
voltage and current, further frequencies can be observed, which are not an integer
of the fundamental.” They appear as discrete frequencies or as a wide-band spec-
trum. A more recent definition is any frequency that is not an integer multiple of the
fundamental frequency (Chapter 1).
5.1.1 Subsynchronous Interharmonics (Subharmonics)
A group of harmonics which are characterized by h < 1, that is, these groups have
periods larger than the fundamental frequency and have been commonly called sub-
synchronous frequency components or subsynchronous interharmonics. In earlier
documents, these were called subharmonics. The term subharmonic is popular in the
engineering community, but it has no official definition. Also see IEEE task force on
harmonic modeling and simulation [2]. IEEE Standard 519 does not address inter-
harmonics but there are many publications on this subject.
5.2 SOURCES OF INTERHARMONICS
Cycloconverters are a major source of interharmonics. Large mill motor drives using
cycloconverters ranging up to 8 MVA appeared in the 1970s. In 1995, rolling mill
drives of 56 MVA were installed. These are also used in 25-Hz railroad traction power
applications. See Chapter 4 for waveforms and an expression for harmonic genera-
tion. The cycloconverters can be thought of as frequency converters. The DC voltage
is modulated by the output frequency of the converter and interharmonic currents
appear in the input, as discussed further.
Electrical arc furnaces (EAF) are another major source. Arcing devices give
rise to interharmonics. These include arc welders. These loads are associated with
low-frequency voltage fluctuations giving rise to flicker. These also exhibit higher
frequency interharmonic components. The interharmonic limits must be accounted
for in filter designs. Other sources are as follows:
Power System Harmonics and Passive Filter Designs, First Edition. J.C. Das.
© 2015 The Institute of Electrical and Electronics Engineers, Inc. Published 2015 by John Wiley & Sons, Inc.
183

184 CHAPTER 5 INTERHARMONICS AND FLICKER
• Induction furnaces
• Integral cycle control
• Low-frequency power line carrier; ripple control
• HVDC
• Traction drives
• ASDs
• Slip frequency recovery schemes
5.2.1 Imperfect System Conditions
Practically, the ideal conditions of operation are not obtained, which give rise to non-
characteristic harmonics and interharmonics. Consider the following:
• The AC system three-phase voltages are not perfectly balanced. The utilities
and industrial power systems have some single phase loads also, which give
rise to unbalance. A 1% lower voltage in one phase will give approximately
7% third and 4.3% fifth harmonics in a standard 12-pulse converter.
• The impedances in the three phases are not exactly equal, especially unequal
commutation reactances or unequal phase impedances of the converter
transformer.
• With a commutating reactance of 0.20 pu and variation of 7.5% in each phase,
firing angle 15∘ will give a fifth harmonic of 33% of fundamental.
• DC modulation and cross modulation. Addition of a harmonic h on DC side
will transfer to AC side; the harmonic will be of different order but of same
phase sequence. The back-to-back frequency conversion represents the worst
case of interharmonic generation. Consider that two AC systems are intercon-
nected through a DC link and operate at different frequencies. An equivalent
circuit can be shown as in Fig. 5.1. The source of ripple in this figure is voltage
from the remote end of the DC link and the distortion caused by the converter
itself, the ripple current depending on the DC-link reactor. The system can rep-
resent HVDC link, the AC power systems operating at different frequencies,
see Section 5.2.3.
A conventional six-pulse three-phase bridge circuit can be conceived as a com-
bination of a switching function and a modulating function. The switching function
can be termed as
s(t) = k
[
cos 𝜔1t −
1
5
cos 5𝜔1t +
1
7
cos 7𝜔1t − ....
]
(5.1)
and the modulating function as the sum of DC current and superimposed ripple
content:
i(t) = Id
∞
∑
z=1
az sin(𝜔zt + 𝜑) (5.2)

5.2 SOURCES OF INTERHARMONICS 185
60 Hz
50 Hz
DC reactor
Rect Inv
Figure 5.1 Two AC systems connected through a DC-link equivalent circuit.
where az is peak magnitude of sinusoidal components and 𝜔z can be of any value and
not an integer multiple of 𝜔1. Then the harmonics on AC side are as follows:
iAC(t) = i(t)s(t) (5.3)
For a 12-pulse operation, following equations can be written for the harmonics on the
AC side:
iAC = kid(12th, 13th, 23rd, … )
+
kb
2
[sin(𝜔1t + 12𝜔2t + 𝜙12) − sin(𝜔1t − 12𝜔2t − 𝜙12)]
−
kb
22
[sin(11𝜔1t + 12𝜔2t + 𝜙12) − sin(11𝜔1t − 12𝜔2t − 𝜙12)]
+
kb
26
−
kc
46
+
kc
50
−
kd
70
etc … (5.4)
where k = 2
√
3𝜋, b, c, and d are the magnitudes of the 12th, 24th, and 36th harmonic
currents on the DC side.
In a rectifier–DC link–converter system linking two isolated AC systems if the
frequency on two sides differ by Δf0, then for a 12-pulse system, the DC-side voltage
at frequency of 12n(f0 + Δf0) will be modulated by another converter:
(12m ± 1)f0 + 12n(f0 + Δf0) (5.5)

On the AC side, among other frequencies, includes the frequency
f0 + 12nΔf0 (5.6)
This will beat with the fundamental component at a frequency of 12nΔf0, which will
allow flicker-producing currents to flow.
The control systems and gate control of the electronic switching devices are
not perfectly symmetrical; these concepts are continued in Chapter 14. These sys-
tem conditions will give rise to noncharacteristics and interharmonics, which would
have been absent if the systems were perfectly symmetrical; a discussion continues
in Chapter 14.
5.2.2 Interharmonics from ASDs
The interharmonics can originate from the converters by interaction of a harmonic
from the DC link into the power source. A harmonic of the order 150 Hz reacting
with fundamental frequency of 60 Hz produces a current wave shape as shown in
Fig. 5.2, the subtraction and addition of two components occur periodically (EMTP
simulation).
Consider an ASD with the motor running at 44 Hz; this frequency will be
present at the DC link as a ripple of 44 Hz times the pulse number of the inverter.
The current on the DC link contains both the 60 Hz and 44 Hz ripples. The 44 Hz rip-
ples will pass on to the supply side and present themselves as interharmonics because
44 times the pulse number is not an integer of 60 Hz.
−40
0 10 20 30
60 Hz
150 Hz
40 50
t (ms)
60 70 80 90 100
−30
−20
−10
0
10
Magnitude
20
30
40
Figure 5.2 Interaction of two harmonic frequencies of differing magnitude, EMTP
simulation.

Ea
Eb
Ec
n o
Ls
Rs
Rd Rm Lm EA
EB
PWM
IGBT
EC
Ld
Vd
Figure 5.3 An ASD circuit with front-end diode-bridge circuit, DC-link reactor, and PWM
inverter.
TABLE 5.1 Interharmonic Current Level and Load Current
Unbalance Measured in a Small Typical Drive
Load Current
Unbalance (%)
Ratio of Source Interharmonic
Current to Fundamental current
0.019 0.000
0.166 0.037
0.328 0.046
0.511 0.065
0.551 0.075
Source: Ref. [3].
If m is the mth motor harmonic and nth is the PWM inverter harmonic and
𝜔 is the inverter operating frequency, then significant components of inverter input
current will exist at frequencies (n ± m)𝜔 for n with a significant switching frequency
component and m with a significant motor harmonic current component.
Consider an ASD system with front-end diode-bridge rectifier, DC-link reactor,
and a PWM inverter (Fig. 5.3). Harmonic currents of the inverter create interharmon-
ics in the power system when these propagate through the DC link.
For balanced cases with linear modulation of the inverter, the DC-link harmon-
ics are of the high order, which are blocked by the DC inductor.
With unbalanced loads or overmodulation, significant amount of interharmon-
ics are generated. A relationship between interharmonic current level and load unbal-
ance is shown in Table 5.1. The load current unbalance can be defined as the difference
between the maximum and minimum phase current magnitudes divided by the aver-
age of the phase current magnitudes. The frequency modulation index mf was chosen
so that the switching frequency is in the range 1.8–2 kHz and amplitude modulation
ratio ma = VAN∕(0.5Vd). With balanced loads and linear modulation, the motor har-
monics begin at switching frequency, and as these were well above DC-link resonant
frequency of 92 Hz, no significant amount of inverter harmonics are present in the
power system.

The unbalance causes low-order harmonics particularly the second and 12th,
Ref [3]. The second and 12th inverter current harmonics in the DC link cause inter-
harmonics when reflected to the AC side of the rectifier:
fh = |𝜇f1 ± kfs| (5.7)
fh is the frequency of the interharmonic, 𝜇 is the order of current harmonic,
typically 2 or 12.
fI is the inverter operating frequency, k = 1, 5, 7, …
fs is the source frequency = 60 Hz.
The most significant values of interharmonics will occur with 𝜇 = 2 and k = 1
(Fig. 5.4). For inverter frequencies of 25, 37.5, and 48 Hz and source frequency of
60 Hz, the side band pairs are 10 and 110, 15 and 135, and 36 and 156 Hz, respectively.
The frequency modulation rate mf was chosen so that switching frequency is in the
range 1.8-2 kHz.
With overmodulation, ma > 1, lower order harmonics appear on the DC link
in balanced case, most dominant being sixth harmonic. When it is reflected to the
AC side, interharmonics at 228 and 348 Hz occur with inverter operating frequency
0
0
20
40
60
80
4 8 12
Percent ratio of motor negative
to positive sequence current
Percent
source
interharmonic
current
48.0 Hz
ma/mf = 0.80/39
37.5 Hz
25 Hz
ma/mf = 0.6250/51
ma/mf = 0.4167/75
Figure 5.4 Generation of current interharmonics in an ASD as a function of unbalance
ratio. Source: Ref. [3].

0.1
1
10
100
RMS
current,
A
(log
scale)
1000 1 Av
103.75
Hz
24.04
A
131.25
Hz
12.04
A
139.375
Hz
5.41
A
260.625
Hz
7.73
A
0% overlap Fundamental frequency = 39.375 Hz
0
Harmonic
order
Interharmonic
order
50 100 150 200 250 300 350 400 450 500 Hz
6f
1
–7f
2
12f
1
–13f
2
6f
1
–
5f
2
6f
1
–
11f
2
12
f
1
–
11f
2
6f
1
–
13f
2
6
f
1
+5
f
2
6
f
1
–f
2
6
f
1
+f
2
1st 5th 7th 11th
V
V
V
V
V
V V
V
V
V
Figure 5.5 Harmonic spectrum from an actual ASD. Source: Ref. [4].
of 48 Hz. This assumes that the DC reactance is substantial and source inductance is
negligible. As Ld is reduced, the rectifier current harmonics rise till the rectifier output
current becomes discontinuous (Chapter 4). The effect of the source inductance will
be to change apparent DC-link inductance and therefore the tuning of the DC-link
components [3].
An example of harmonic spectrum from an actual operating system is shown
in Fig. 5.5 [4]. The motor is fed at 39.4 Hz (50-Hz source frequency). If the har-
monics or interharmonics coincide with the natural frequency of the motor/shaft/load
mechanical system, then shaft damage is possible.
5.2.3 HVDC Systems
HVDC systems are another possible source of interharmonics. Interharmonics of the
order of 0.1% of the rated current can be expected in HVDC systems, when two
ends are working at even slightly different frequencies [5,6]. Referring to Fig. 5.1,
following harmonics are generated considering six-pulse converters at either end.
The modulation theory has been used in harmonic interactions in HVDC sys-
tems (see also Chapters 12 and 14). When AC networks operate at different frequen-
cies, interharmonics will be produced.
DC Side The voltage harmonics will contain frequency groups 6n𝜔1 and
(6n𝜔1 + 𝜔m):

where 𝜔m is the mth harmonic frequency, which may be an integer harmonic of either
of the two AC systems – call it a disturbing frequency.
The characteristic harmonics in DC voltage (= 6n𝜔1) appear in DC current.
Harmonic frequencies will be 𝜔m = 6m𝜔2. This gives a new group of harmonics:
6n𝜔1 ± 6m𝜔1 = 6(n ± m)𝜔1 = 6k𝜔1 (5.8)
where n, m, and k are integers.
All characteristic harmonics from the inverter will appear in the DC current
and the frequency will be 6m𝜔2. Thus, second group of harmonics on DC side are as
follows:
6n𝜔1 ± 6m𝜔2 = 6(n𝜔1 ± m𝜔2) (5.9)
The third set of frequencies from Eq. (5.9) will also appear in the DC current, so that
𝜔m = 6(n𝜔1 ± p𝜔2); and therefore, the frequencies are
6n𝜔1 ± 6(m𝜔1 ± p𝜔2) = 6[(n ± m)𝜔1 ± p𝜔2)] = 6(k𝜔1 ± p𝜔2) (5.10)
where n, m, p, k are integers.
AC Side The harmonics on the AC side will be the following:
Those caused by DC characteristic harmonics, 𝜔m = 6m𝜔1. The harmonics
transferred to AC side are as follows:
6m𝜔1 ± (6n ± 1)𝜔1 = (6k ± 1)𝜔1 (5.11)
Those caused by characteristic DC voltage harmonics generated at far end 𝜔m =
6m𝜔2
6m𝜔2 ± (6n ± 1)𝜔1 (5.12)
Those caused by
𝜔m = 6(m𝜔1 ± p𝜔2) (5.13)
The harmonics transferred to AC side will be
6(m𝜔1 ± p𝜔2) ± (6n ± 1)𝜔1 (5.14)
This assumes low DC-side impedance (also see Ref. [7,8]). Practically, DC-link reac-
tor and AC and DC filters are used to mitigate the harmonics (Chapter 15).
The interharmonics due to Kramer drives, wind power generation, and electric
traction are discussed in Chapter 4.

5.2.4 Cycloconverters
Cycloconverters are discussed in Chapter 4. Certain relationship exists between the
converter pulse numbers, the harmonic frequencies present in the output voltage, and
the input current. The harmonic frequencies in the output voltage are the integer mul-
tiple of pulse number and input frequency, (np)f, to which are added and subtracted
integer multiple of output frequency, that is,
houtput voltage = (np)f ± mf0 (5.15)
Here, n is any integer and not the order of the harmonic, and m is also an integer as
described later.
For cycloconverter with single-phase output, the harmonic frequencies present
in the input current are related to those in the output voltage. There are two families
of input harmonics:
hinput current = |[(np) − 1] f ± (m − 1)f0|
hinput current = |[(np) + 1] f ± (m − 1)f0| (5.16)
where m is odd for (np) even and m is even for (np) odd.
In addition, the characteristic family of harmonics independent of pulse number
is given by
|f ± 2mf0| m ≥ 1 (5.17)
For a cycloconverter with a balanced three-phase output, for each family of output
voltage harmonics, (np)f ± mf0, there are two families of input current harmonics:
hinput current = |[(np) − 1] f ± 3(m − 1)f0|
hinput current = |[(hp) + 1]f ± 3(m − 1)f0| (5.18)
where m is odd for (np) even and m is even for (np) odd.
In addition, the characteristic family of harmonics independent of pulse number
is given by
|f ± 6mf0| m ≥ 1 (5.19)
Figure 5.6 shows a chart of relationships between the predominant harmonic fre-
quencies present in a three-phase input current waveform of the cycloconverter with
a balanced three-phase output, and output to input frequency ratio. For input current
waveforms with higher pulse numbers, certain harmonic families are eliminated as
shown [9].
The magnitude of the harmonic is a function of the output voltage and the load
displacement angle, but is independent of the frequency of the component. Thus, for
a given output voltage ratio and load displacement angle, those harmonic components
that are present always have the same relative magnitude independent of pulse number
or the number of output phases.

These families of harmonic
frequencies are present in
3- and 9-pulse
input current waveforms
3-, 6-, and 12-pulse
3- and 6-pulse
the 3-pulse
input current waveform
Characteristic cyctoconverter
harmonic frequencies
This family is present,
independent of the
pulse number of the
current waveform
fH
13fi
11fi
13fi – 6fo
11f i
+ 6f o
10fi – 3fo
10fi
+ 3fo
8fi
+ 3fo
5f i
+ 6f o
4fi – 3fo
4fi
+ 3fo
2fi
+ 3fo
2fi – 3fo
fi – 6fo
f i
+ 6f o
8fi – 3fo
7f i
+ 6f o
7fi + 6fo
7fi
5fi
fi
13
11
10
8
7
5
4
2
1
0 0.1 0.2 0.3 0.4
Fundamental fi
0.5 0.6 0.7 0.8 0.9 1.0
11fi + 6fo
5fi – 6fo
Figure 5.6 Chart showing the relationship between predominant harmonic frequencies
present in a three-phase input current waveform of the cycloconverter with a balanced
three-phase output, and the output-to-input frequency ratio. For input current waveforms with
higher pulse numbers, certain harmonic families are eliminated as indicated. Source: Ref. [9].
5.3 ARC FURNACES
A schematic diagram of an EAF installation is shown in Fig. 5.7. The furnace is gen-
erally operated with static var compensation systems and passive shunt harmonic fil-
ters (Chapter 15). The installations can compensate rapidly changing reactive power
demand, arrest voltage fluctuations, reduce flicker and harmonics, and simultaneously
improve the power factor to unity. Typical harmonic emissions from IEEE Standard
519 are shown in Table 4.6. In practice, a large variation in harmonics is noted. For
example, maximum to minimum limits of voltage distortions at second, third, and
fourth harmonics may vary from 17% to 5%, 29% to 20%, and 7.5% to 3%, respec-
tively. The tap-to-tap time (the time for one cycle operation, melting, refining, tipping,
and recharging) may vary between 20 and 60 min depending on the processes, and

5.3 ARC FURNACES 193
HV source
Source
impedance
Secondary cables
and bus
TCR, Filters
Main step down
transformer
EAF transformer
Rarc
Figure 5.7 Schematic diagram of an EAF installation.
0
50 100 150 200
Frequency (Hz)
250 300 350 400
10
20
30
Percentage
of
50
Hz
component
40
50
100%
Figure 5.8 Typical spectrum of harmonic and interharmonic emissions from an EAF.
the furnace transformer is de-energized and then re-energized during this operation.
This gives rise to additional harmonics during switching; saturation of transformer
due to DC and second harmonic components, dynamic stresses, can bring about res-
onant conditions with improperly designed passive filters. New technologies such as
STATCOM, see Section 5.8.1, and active filters can be applied.
Figure 5.8 shows a typical spectrum of harmonic and interharmonic emission
from an arc furnace (50 Hz power supply frequency) and Fig. 5.9 is a plot of inter-
harmonic emission from EAF [10].
A typical filter configuration to avoid magnifying interharmonics is illustrated
in Fig. 5.10. The resistors provide damping to prevent magnification of interharmon-
ics components. Type C filters are commonly employed (see Chapter 15 for the filter
types).
Figure 5.11 is based on Ref. [11]. The second harmonic filter is essentially
a type C filter (see Chapter 15). The resistor RD remains permanently connected.

1
2
3
4
Ilh / I1 (%)
2 3 4 5
Harmonic order
6 7 8 9
Figure 5.9 A plot of
interharmonic emission
form EAF. Source: Ref.
[10].
Third order filter
hT = 3.1
High pass filter
hT = 5.1
High pass filter
hT = 7.0
High pass filter
hT = 10.5
Figure 5.10 A typical harmonic filter configuration to avoid magnification of
interharmonics in EAF.
High damping is needed during transformer energization in order to reduce stresses
on the elements of harmonic filters. This is achieved by connecting a low resistance
RTS in parallel with RD during energization for a short time. The damping of transients
becomes an important consideration, also see Chapter 16 for a case study.
The following harmonic restrictions from EAFs are from Ref. [12]. It assumes
a PCC < 161 kV and SCR < 50.
• Individual integer harmonic components (even and odd) should be less than 2%
of the specified demand current for the facility, 95% point on the cumulative
probability distribution.

5.3 ARC FURNACES 195
Utility tie transformer
Furnace transformers
TCR (32 Mvar)
C1
RD RTS
L
C2
(cable impedances not shown)
Second harmonic
filter 14.2 Mvar
Third harmonic
filter, 16 Mvar
13.8 kV bus, secondary of
50 MVA utility transformer, primary
of furnace transformers
PCC
Figure 5.11 A configuration for harmonic emission control with type C filter and damping
of transformer inrush current harmonics. Source: Ref. [11].
• Individual noninteger distortion components (interharmonics) should not
exceed 0.5% of the specified demand current of the facility, 95% point on the
cumulative probability distribution.
• The total demand distortion at the point of common coupling (PCC) should be
limited to 2.5%, 95% point on the cumulative probability distribution. Addi-
tional restrictions should be applied to limit shorter duration harmonic levels,
if it is determined that they could excite resonance in the power supply system
or cause problem at local generators. This can be done by specifying separate
limits that are only exceeded 1% of the time (usually not necessary).
5.3.1 Induction Furnaces
A system configuration of the induction furnace is shown in Fig. 5.12. It depicts a
12-pulse rectification with H-bridge inverter (see Chapter 6) and induction furnace
load. The measurement data in this configuration are for 25-t, 12-MVA IMF (induc-
tion melting furnace) from Ref. [13]. A typical time-varying supply-side current dur-
ing one melting cycle is shown in Fig. 5.13. The harmonics and interharmonics may
interact with the industrial loads or passive filters and may be amplified by resonance
with the passive filters. A model is generated, and the variable frequency operation
is represented by a time-varying R–L circuit in parallel with a current source. The
results of the measurements are shown in Fig. 5.14. Here, type A measurements show
interharmonics due to cross modulation of the fundamental power supply frequency
f and the inverter output frequency referred to the DC link, 2fo. Type B measurements
are cross modulation of the fundamental frequency at the DC link at 2kfo, where fo is

HV
source
Source
impedance
Step-down
transformer Harmonic
filters
12-pulse
rectifier
Inverter
Induction furnace
load
LDC
MV-bus
Figure 5.12 A system configuration for an induction furnace.
0
0
20
40
60
80
100
120
1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 0
0
5
10
Amplitude
(A)
15
20
25
30
Time (min)
Frequency (Hz)
ISI, multiply by 10
5
10
15
Amplitude
(A)
20
25
30
Figure 5.13 Typical time-varying supply-side current during melting cycle of a 12-MVA,
25-t induction furnace. Source: Ref. [13].
the output frequency of the inverter. Type C is the cross modulation of the harmonic
current frequencies at (12h ± 1)f and the DC-link harmonic frequency 2fo.
5.4 EFFECTS OF INTERHARMONICS
The interharmonic frequency components greater than the power frequency produce
heating effects similar to those produced by harmonics. The low-frequency voltage
interharmonics cause significant additional loss in induction motors stator windings.
The impact on light flicker is important. Modulation of power system voltage
with interharmonic voltage introduces variations in system voltage rms value.
The IEC flickermeter is used to measure the light flicker indirectly by simu-
lating the response of an incandescent lamp and human-eye-brain response to visual
stimuli, IEC Standard [14]. The other impacts of concern are as follows:
• Excitation of subsynchronous conditions in turbogenerator shafts.
• Interharmonic voltage distortions similar to other harmonics.
• Interference with low-frequency power line carrier control signals.

5.4 EFFECTS OF INTERHARMONICS 197
120
1400 1200 1000 800 600
Frequency (Hz)
400 200 0
Time (min)
90
60
30
0
0
5
10
15
20
25
30
Current
harmonic
amplitude
Fundamental
TYPE A
TYPE C
TYPE B
TYPE B
25th 23th
13th
11th
TYPE C
Figure 5.14 Interharmonics due to cross modulation, see text for types A, B, and C
harmonic emissions shown in this figure. Source: Ref. [13].
• Overloading of conventional-tuned filters. See Chapter 15 for the limitations
of the passive filters, the tuning frequencies, the displaced frequencies, and
possibility of a resonance with the series-tuned frequency. As the interharmon-
ics vary with the operating frequency of a cycloconverter, a resonance can be
brought where none existed before making the design of single-tuned filters
impractical.
The distortion indices for the interharmonics can be described similar to indices
for harmonics. The total interharmonic distortion (THID) factor (voltage) is
THID =
√
n
∑
i=1
V2
i
V1
(5.20)
where i is the total number of interharmonics being considered including subharmon-
ics, and n is the total number of frequency bins. A factor exclusively for subharmonics
can be defined as total subharmonic distortion factor:
TSHD =
√
√
√
√
S
∑
s=1
V2
s
V1
(5.21)
An important consideration is that torsional interaction may develop at the nearby
generating facilities (see Section 5.10). In this case, it is necessary to impose severe
restrictions on interharmonic components. In other cases, interharmonics need not be
treated any different from integer harmonics.

5.5 REDUCTION OF INTERHARMONICS
The interharmonics can be controlled by
• Higher pulse numbers
• DC filters, active or passive, to reduce the ripple content
• Size of the DC-link reactor
• Pulse width modulated drives
5.6 FLICKER
Voltage flicker occurs due to operation of rapidly varying loads, such as arc furnaces
that affect the system voltage. This can cause annoyance by causing visible light
flicker on tungsten filament lamps. The human eye is most sensitive to light variations
in the frequency range 5–10 Hz and voltage variations of less than 0.5%, and this
frequency can cause annoying flicker from tungsten lamp lighting.
5.6.1 Perceptible Limits
The percentage pulsation of voltage related to frequency, at which it is most percep-
tible, from various references, is included in Fig. 5.15 of Ref [15]. In this figure,
the solid lines are composite curves of voltage flicker by General Electric Com-
pany (General Electric Review, 1925); Kansas Power and Light Company, Electrical
World, May 19, 1934; T7D Committee EEI, October 14, 1934, Chicago; Detroit
Edison Company; West Pennsylvania Power Company; and Public Service Company
0
1
2
3
4
5
Percentage
of
voltage
fluctuations
Fluctuations per hour
Border line
of visibility
Border lines
of irritation
House pumps, sump pumps
A/C equipment
Theatrical lighting
Domestic refrigerators
Oil burners
Single elevator
Hoists
Cranes
Y-delta changes on
Elevator MG sets
X-ray equipment
Arc furnaces
Flashing signs
Arc welders
Manual spot welders
Drop hammers
Saws
Group elevators
Reciprocating pumps
Compressors
Automatic
Spot welders
Fluctuations per minute Fluctuations per sec
30 60 15
2
1
1
Figure 5.15 Maximum permissible voltage fluctuations see explanations in text. Source:
Ref. [15].

5.6 FLICKER 199
0.01
0.1
1
ΔV
(%)
10
0.1
IEEE
IEC
1 10 100
Changes per minute
1000 10000
Figure 5.16 Comparison
of IEC and IEEE standards
with respect to flicker
tolerance. Source: Ref.
[16].
of North Illinois. Dotted lines show voltage flicker allowed by two utilities, reference
Electrical World November 3, 1958, and June 1961. The flicker depends on the whole
chain of “voltage fluctuations-luminance-eyes-brain.”
Though this figure has been in use for a long time, it was superseded in IEEE
Standard 1453, Ref [16] with Fig. 5.16. The solid-state compensators and loads may
produce modulation of the voltage magnitude that is more complex than what was
envisaged in the original flicker curves. This standard adopts IEC Standard 61000-3-3
[17] in total. Define
Plt = 3
√
√
√
√ 1
12
∗
12
∑
j=1
Pst
3
j (5.22)
where Plt is a measure of long-term perception of flicker obtained for a 2-h period.
This is made up of 12 consecutive Pst values, where Pst is a measure of short-term
perception of flicker for 10-min interval. This value is the standard output of IEC
flickermeter. Further qualification is that IEC flickermeter is suited to events that occur
once per hour or more often. The curves in Fig. 5.15 are still useful for infrequent
events similar to a motor start, once per day, or even as frequent as some residential
air conditioning equipment. Figure 5.16 depicts comparison of IEEE and IEC for
flicker irritation.
The short-term flicker severity is suitable for accessing the disturbances caused
by individual sources with a short duty cycle. When the combined effect of several
disturbing loads operating randomly is required, it is necessary to provide a criterion
for long-term flicker severity, Plt. For this purpose, the Plt is derived from short-term
severity values over an appropriate period related to the duty cycle of the load, over
which an observer may react to flicker.
For acceptance of flicker causing loads to utility systems, IEC standards
[17–19] are recommended. The application of shape factors allows the effect of loads
with voltage fluctuations other than the rectangular to be evaluated in terms of Pst
values. Further research is needed to investigate effects of interharmonics on flicker
and flicker transfer coefficients from HV to LV electrical power systems [20,21].

5.6.2 Planning and Compatibility Levels
Two levels: Planning level and compatibility levels are defined. Compatibility level
is the specified disturbance level in a specified environment for coordination in set-
ting the emission and immunity limits. Planning level, in a particular environment,
is adopted as a reference value for limits to be set for the emissions from large loads
and installations, in order to coordinate these limits with all the limits adopted for
equipment intended to be connected to the power supply system.
As an example, planning levels for Pst and Plt in MV (voltages > 1 kV and
< 35 kV), HV (voltages > 35 kV and < 230 kV), and EHV (voltages > 230 kV)
are shown in Table 5.2, and compatibility levels for LV and MV power systems are
shown in Table 5.3.
5.6.3 Flicker Caused by Arcing Loads
Arc furnaces cause flicker because the current drawn during melting and refining
periods is erratic and fluctuates widely and the power factor is low (Chapter 4). An
EAF current profile during melting and refining is depicted in Fig. 5.17; see also
Fig. 1.3 for the erratic nature of the current. Figure 5.18(a) shows flicker perception
level Pfs, with respect to voltage variation, while Fig. 5.18(b) shows Pst for a certain
source impedance, assumed constant, and Fig. 5.19 depicts Pfs, Pst, Plt, and voltage
variations.
There are certain other loads that can also generate flicker, for example, large
spot welding machines often operate close to the flicker perception limits. Industrial
processes may comprise a number of motors having rapidly varying loads or start-
ing at regular intervals, and even domestic appliances such as cookers and washing
machines can cause flicker on weak systems. However, the harshest load for flicker
TABLE 5.2 Planning Levels for Pst and Plt in MV,
HV, and EHV Power Systems
Planning Levels
MV HV-EHV
Pst 0.9 0.8
Plt 0.7 0.6
Source: Ref. [16].
TABLE 5.3 Compatibility Levels for Pst and Plt in LV
and MV Systems
Compatibility Level
Pst 1.0
Plt 0.8
Source: Ref. [16].

5.6 FLICKER 201
0
Current
(A)
Current
(A)
60 120 240 360
Frequency (Hz)
(b)
(a)
420 600
Figure 5.17 Erratic current spectrum of an EAF during (a) melting and (b) refining.
is an arc furnace. During the melting cycle of a furnace, the reactive power demand
is high. Figure 5.17 shows that an arc furnace current is random and no periodic-
ity can be assigned, yet some harmonic spectra have been established, Table 4.6,
from IEEE 519. Note that even harmonics are produced during melting stage. The
high reactive power demand and poor power factor causes cyclic voltage drops in the
supply system. Reactive power flow in an inductive element requires voltage differ-
ential between sending end and receiving ends, and there is reactive power loss in the
element itself. When the reactive power demand is erratic, it causes corresponding
swings in the voltage dips, much depending on the stiffness of the system behind the
application of the erratic load. This voltage drop is proportional to the short-circuit
MVA of the supply system and the arc furnace load.
For a furnace installation, the short-circuit voltage depression (SCVD) is
defined as
SCVD =
2MWfurnace
MVASC
(5.23)
where the installed load of the furnace in MW is MWfurnace and MVASC is the
short-circuit level of the utility’s supply system. This gives an idea whether potential
problems with flicker can be expected. An SCVD of 0.02–0.025 may be in the
acceptable zone, between 0.03 and 0.035 in the borderline zone, and above 0.035
objectionable [22]. When there are multiple furnaces, these can be grouped into
one equivalent MW. A case study in Chapter 16 describes the use of tuned filters to
compensate for the reactive power requirements of an arc furnace installation. The
worst flicker occurs during the first 5–10 min of each heating cycle and decreases as
the ratio of the solid to liquid metal decreases.

Voltage
Pfs
Time
(a)
(b)
0
0 10 20 30 40 50 60
Time (minutes)
3
6
9
12
Flicker
(Pst)
15
18
Figure 5.18 (a) Flicker perception level; (b) Measured short-term flicker of an EAF, source
impedance considered time invariant.
The significance of ΔV∕V and number of voltage changes are illustrated with
reference to Fig. 5.20 from IEC [14]. This shows a 50-Hz waveform, having a 1.0
average voltage with a relative voltage change Δv∕ v = 40% and with 8.8-Hz rectan-
gular modulation. It can be written as
v(t) = 1 × sin(2𝜋 × 50t) ×
{
1 +
40
100
×
1
2
× signum [2𝜋 × 8.8 × t]
}
(5.24)
Each full period produces two distinct changes: one with increasing magnitude and
one with decreasing magnitude. Two changes per period with a frequency of 8.8 Hz
give rise to 17.6 changes per second.
5.7 FLICKER TESTING
The European test of flicker is designed for 230-V, 50-Hz power and the limits
specified in IEC are based on the subjective severity of flicker from 230-V/60-W

5.7 FLICKER TESTING 203
Pst
PIt
Pfs
Voltage
0 1 2 3 4
Time (hours)
5 6
Figure 5.19 Measurement of short-term flicker at a medium voltage bus.
−1.5
0 0.05 0.1 0.15 0.2 0.25
Time (s)
ν = 1.0 Δν = 0.4
0.3 0.35 0.4
−1.0
−0.5
0
0.5
Voltage
normalized
(V)
0.8
1.0
1.2
1.5
Figure 5.20 Modulation
with rectangular voltage
change ΔV∕V = 40%,
8.8 Hz, 17.6 changes per
second. Source: Ref. [14].
coiled–coil filament lamps and fluctuations of the supply voltage. In the United
States, the lighting circuits are connected at 115–120 V. For a three-phase system,
a reference impedance of 0.4 + j0.25 ohms, line to neutral, is recommended, and
IEC Standard 61000-3-3 is for equipments with currents ≤16 A. The corresponding
values in the United States could be 32 A; a statistical data of the impedance up to
the PCC (Point of Common Coupling) with other consumers is required. As for a
115-V system, the current doubles, the authors in Ref [23] recommend a reference
impedance of 0.2 + j0.15 ohms.

t1
10 ms
t2 t3
Ut
Uc max
Max
voltage
change
Figure 5.21 To explain the IEC terminology for the calculation of Pst.
An explanation of some terms used in IEC terminology is
ΔU(t) Voltage change characteristics. The time function of change in
rms voltage between periods when the voltage is in a
steady-state condition for at least 1 s.
U(t) rms, voltage shape. The time function of the rms voltage
evaluated stepwise over successive half-periods of the
fundamental voltage.
Δ Umax Maximum voltage change. The difference between maximum and
minimum rms voltage change characteristics.
ΔUc Steady-state voltage change. The difference between maximum
and minimum rms values of voltage change characteristics.
d(t), dmax, dc Ratios of the magnitudes of ΔU(t), Δ Umax, ΔUc to the phase
voltage.
See Fig. 5.21.
The expression shown below is used for Pst based on an observation period
Tst = 10 min.
Pst =
√
0.0314P0.1 + 0.0525P1s + 0.0657P3s + 0.28P10s + 0.08P50s (5.25)
where percentiles P0.1, P1s, P3s, P10s, P50s are the flicker levels exceeded for 0.1%,
1%, 3%, 10%, and 50% of the time during the observation period. The suffix “s”
indicates that the smoothed value should be used, which is obtained as follows:
P50s = (P30 + P50 + P80)∕3
P10s = (P6 + P8 + P10 + P13 + P17)∕5

5.8 CONTROL OF FLICKER 205
P3s = (P2.2 + P3 + P4)∕3
P1s = (P0.7 + P1 + P1.5)∕3 (5.26)
5.8 CONTROL OF FLICKER
The response of the passive compensating devices is slow. When it is essential to
compensate load fluctuations within a few milliseconds, SVCs are required. Referring
to Fig. 4.25, large TCR flicker compensators of 200 MW have been installed for arc
furnace installations. Closed-loop control is necessary due to the randomness of load
variations, and complex circuitry is required to achieve response times of less than
one cycle. Significant harmonic distortion may be generated, and harmonic filters will
be required. TSCs (thyristor-switched capacitors [23]) have also been installed and
these have inherently one cycle delay as the capacitors can only be switched when
their terminal voltage matches the system voltage. Thus, the response time is slower.
SVCs employing TSCs do not generate harmonics, but the resonance with the system
and transformer needs to be checked.
If the voltage to the load is corrected fast and maintained constant, the flicker
can be eliminated. Figure 5.22 shows an equivalent circuit diagram and the phasor
diagram. The objective is to keep VL constant by injecting variable voltage Vc to
compensate for the voltage drop in the source impedance due to flow of highly erratic
current Is.
5.8.1 STATCOM for Control of Flicker
It has been long recognized that reactive power can be generated without use of bulk
capacitors and reactors and STATCOM (static compensator) also called STATCON
(static condenser) makes it possible. It is capable of operating with leading or lagging
power factors. Its operation can be described with reference to Fig. 5.23, which
depicts a synchronous voltage source. A solid-state synchronous voltage source
abbreviated as SS is analogous to a synchronous machine and can be implemented
with a voltage source inverter using GTOs (gate turn-off thyristors). The reactive
power exchange between the inverter and AC system can be controlled by varying the
amplitude of the three-phase voltage produced by the SS. Similarly, the real power
exchange between the inverter and AC system can be controlled by phase shifting
the output voltage of the inverter with respect to the AC system. Figure 5.23(a)
shows a rotating synchronous condenser. No reversal of power is possible, it can
absorb only limited capacitive current from the system, filed current cannot be
reversed. Figure 5.23(b) shows a STATCOM, the coupling transformer, the inverter,
and an energy source that can be a DC capacitor, battery, or superconducting magnet.
The reactive and real power generated by the SS can be controlled independently
and any combination of real power generation/absorption with var generation and
absorption is possible, as shown in Fig. 5.23(c). The real power supplied/absorbed
must be supplied by the storage device, while the reactive power exchanged is
internally generated in the SS. This bidirectional power exchange capability of the

RS RL
VT VL
VC
IS
VS
Load
VL
VC
VS
−VC VL = Constant
locus
ISXS
ISRS
VT
IS
(a)
(b)
Figure 5.22 (a) Equivalent circuit diagram for compensation of load voltage; (b) phasor
diagram.
SS makes complete temporary support of the AC system possible. STATCOM can
be considered as an SS with a storage device as DC capacitor. A GTO-based power
converter produces an AC voltage in phase with the transmission line voltage. When
the voltage source is greater than the line voltage (VL < V0), leading vars are drawn
from the line and the equipment appears as a capacitor; when voltage source is
less than the line voltage (VL > V0), a lagging reactive current is drawn. Using the
principle of harmonic neutralization, the output of n basic six-pulse inverters, with
relative phase displacements, can be combined to produce an overall multiphase
system. The output waveform is nearly sinusoidal and the harmonics present in the
output voltage and input current are small, though not zero, see Table 6.1 for typical
harmonic emission.
With design of high bandwidth control capability, STATCOM can be used to
force three-phase currents of arbitrary wave shape through the line reactance. This
means that it can be made to supply nonsinusoidal, unbalanced, randomly fluctuating
currents demanded by the arc furnace. With a suitable choice of DC capacitor, it
can also supply the fluctuating real power requirements, which cannot be achieved
with SVCs.
The instantaneous reactive power on the source side is the reactive power cir-
culating between the electrical system and the device, while reactive power on the

5.8 CONTROL OF FLICKER 207
AC system
AC terminals
AC terminals
DC terminals
DC terminals
Multi-phase
inverter
DC terminals
Absorbs P
Supplies Q
Absorbs P
and Q
Supplies P
absorbs Q
Supplies P
and Q
No reversal of power, can
absorb limited capacitive
power form the system, no
reversal of exciter current
Energy storage
SM
Field
Exciter
(a)
(b)
(c)
IDC
VDC
−IDC ldc
lp
lq
VDC
Xt
Xt
IAC
IAC
Coupling
transformer and
synchronous
machine
reactance
Coupling transformer
reactance
+
+
Figure 5.23 (a) A rotating condenser; (b) a shunt-connected synchronous voltage source;
(c) possible modes of operation for real and reactive power generation.
output side is the instantaneous reactive power between the device and its load. There
is no relation between the instantaneous reactive powers on the load and source side,
and the instantaneous imaginary power on the input is not equal to the instantaneous
reactive power on the output (Chapter 1). The STATCOM for furnace compensation
may use vector control based on the concepts of instantaneous active and reactive
powers, i𝛼 and i𝛽 (Chapter 1).
Figure 5.24 shows flicker reduction factor as a function of flicker frequency,
STATCOM versus SVC [24]. Flicker mitigation with a fixed reactive power compen-
sator and an active compensator - a hybrid solution for welding processes is described
in [25]. Flicker compensation with series active filters (SAF) and parallel active fil-
ters is also applicable, Ref [26, 27] and Chapter 6. A combination of SAF and shunt

0
0
R
=
1
×
100
5 10 15 20
SVC
STATCOM
Flicker frequency (Hz)
25 30
10
20
30
40
50
Flicker
with
compensator
Flicker
without
compensator
60
70
80
90
100
Figure 5.24 Flicker factor R for a STATCON and SVC.
passive filters is possible, in which SAF behaves like an isolator between the source
and the load. A series capacitor can compensate for the voltage drop due to sys-
tem impedance and fluctuating load demand, thus stabilizing the system voltage and
suppress flicker and noise.
5.9 TRACING METHODS OF FLICKER AND
INTERHARMONICS
Determining each source of flicker and ascertaining how much it contribute to the
flicker at PCC has been studied by many authors [28–32].
5.9.1 Active Power Index Method
The interharmonic active power can be obtained by measurements of voltage and
current at PCC:
PIH = |VIH||IIH| cos(𝜙IH) (5.27)
Consider that a number of consumers are connected to a source served by the utility.
Representing each possible polluting source as a Norton equivalent circuit and carry-
ing out the measurements on the feeder serving the consumer as well supply source,
measurement at point A in Fig. 5.25, the polluting source, can be identified. Any of
the sources can be the polluting source. For point A, if PIH > 0, the interharmonic
component is from the supply system, and if the measured PIH < 0 the interharmonic
component comes from the respective consumer.
Practically, the active power of the interharmonics is small, the angle 𝜙IH may
be close to plus minus 90∘ and the measurements may oscillate. The interharmonic
emissions may not be stable during the measurements.

5.9 TRACING METHODS OF FLICKER AND INTERHARMONICS 209
Utility PCC Load
Zs IH ZL
A
Utility PCC Load
Zs IH
ZL
A
(a) (b)
Figure 5.25 Determination of interharmonic source by Norton’s equivalent: (a)
interharmonic source at PCC is utility; (b) interharmonic source at PCC is the consumer load.
5.9.2 Impedance-Based Method
The harmonic impedance at the metering point can be obtained by
ZIH =
|
|
|
|
VIH
IIH
|
|
|
|
cos(𝜑IH) + j
|
|
|
|
VIH
IIH
|
|
|
|
sin(𝜑IH) = RIH + jXIH (5.28)
The concept is that the interharmonic impedance is either upstream or down-
stream of the measuring point. The system impedance is generally much smaller than
the load-side impedance, almost 1/5th of the source impedance. The magnitude of ZIH
can be checked if it is source-side or load-side impedance. The source impedance is
given by the short-circuit calculations. It can be corrected for the interharmonic by
multiplying with a factor of fIH∕f (neglecting resistance) and the load impedance by
V1∕I1.
If the source impedance after correction for the interharmonic frequency and
ZIH are not of the comparable values, the measured impedance is likely to be down-
stream impedance and the interharmonic source is the supply system.
5.9.3 Reactive Load Current Component Method
The active power and impedance-based methods focus on a major source of flicker,
yet, how much each source contributes to flicker level at PCC is of much interest.
The reactive load current component method is based on the concept that variation
of the fundamental component of the voltage waveform in time causes the amplitude
modulation affect which causes flicker. The background flicker contributed by the
supply source adds to the flicker caused by loads at the PCC.
The system impedance and its angle are not constant quantities, and the values
can be based on measurements.
Also source voltage cannot be assumed constant. Then, a time-varying relation
can be written as
es = iRs + Ls
di
dt
+ vpcc (5.29)
where vpcc is the voltage at PCC.

Vpcc DFT, Vpcc
Zs or Xs
Pst,n
DFT, I(t)
Compute
θ
Compute
ΔV
IEC
Flickermeter
Flicker contribution meter
θ
ln(t)
One cycle
DFT
I
Figure 5.26 A block
circuit diagram of
individual flicker
contribution meter.
Source: Ref [30].
This can be approximated as
Es ≈ VPCC + XsI sin 𝜃 (5.30)
where 𝜃 is the impedance angle.
A block circuit diagram of this method is shown in Fig. 5.26 and the IEC flick-
ermeter block circuit diagram is shown in Fig. 5.27. Reference [30] illustrates flicker
contribution measurements of some sample plants, such as steel plants and EAFs by
the proposed flicker contribution meter.
Reverse power flow procedure to identify the source of harmonics can be used.
Line and bus data at several points in the network are used with a least square esti-
mator to calculate the injection spectrum at buses expected to be harmonic sources.
When energy at harmonic frequencies is found to be injected into the network, then
that bus is identified as a harmonic source.
5.10 TORSIONAL ANALYSIS
Torsional vibrations are responsible for failure of drive system components and can
stress or shear the turbine blades in generating units. Figure 5.28(a) shows a simple
torsional model in steady-state torqued condition at rest or at constant speed. The
electrical torque and the load torque are constant and in balance. There is no relative
motion between the masses, but there is a twist in the shaft, with a spring constant of
K. Note the relative positions of the angles of twist.
If the steady-state torques were removed, the two inertias will vibrate about the
zero torque axes (Fig. 5.28(b)). In the absence of any damping, these vibrations will
continue with peak torque and twist equal to initial steady-state values. The resonant
frequency will be given by

211
Input
transformer
Block 1 Block 2 Block 3 Block 4 Block 5
AND
Converter
sampling rate
≥ 50 Hz.
dB
0
Hz
230 V
50 Hz
120 V
60 Hz
35
42 120 Weighting filters Squaring and
smoothing
Output 2
Weighted voltage
function
Output 3
Range selection
Output 4
Short-time
integration
Output 5
Recording
Output
data display
and recording
Programming of short and
long observation periods
Statistical evaluation of
flicker level
I minute
integrator
Square
rooter
0
0.5
1.0
2.0
5.0
10.0
Squaring
multiplier
First
order
sliding
mean
filter
64
level
classifier
Output
interfaces
20.0
8.8
Range
selector
Hz%
ΔV
V
100
−3
−60
Simulation of brain-eye response
Detector and
gain control
Demodulator
with
squaring
multiplier
Input voltage
adapter
Signal generator
for calibration
checking
RMS
meter
Output 1
Half cycle rms
voltage indication
Figure 5.27 Block circuit diagram of IEC flickermeter.

T
(a)
(b)
T12
θ1
θ2
T
T12
T
T
θ1
Figure 5.28 (a) Torsional model with two shaft-coupled rotating masses under steady state,
constant torque; (b) forced oscillations with torque removed.
f0 =
√
K(J1 + J2)
J1J2
(5.31)
The stored energy in the system is converted to kinetic energy two times per cycle, and
the two inertias oscillate in opposition to each other. If one of the torques is removed,
an oscillation with smaller amplitude will occur.
5.10.1 Steady-State Excitation
Consider that a steady-state excitation of frequency f0 is applied to the system shown
in Fig. 5.28(a). A torsional vibration will be excited and it may continue to grow in
magnitude, till the energy loss per cycle is equal to the energy that the small dis-
turbance adds to the system during a cycle. If the excitation frequency varies at a
certain rate, the torsional vibrations will be amplified as the system passes through
the resonant point [33–35].
In an ASD during normal operation, there are multiples of converter pulse
outputs, that is, for a 12-pulse converter 12×, 24×, 36×, and 48× electrical output
frequency. Figure 5.29 from Ref. [36] identifies where the excitation frequencies
intersect with the torsional natural frequencies. This analysis is for a 15,000-hp,
6000-rpm synchronous motor drive in a petrochemical industry.
The driven load may have a positive slope, that is, the load increases with the
speed. This occurs for fans and blowers. The load may have a negative slope, that is,
conveyers and crushers. If the motor torque is removed, the negative load slope tends
to give increasing torque pulsations.
An induction motor produces transient torques during starting. A synchronous
motor, in addition to the initial fixed-frequency excitation such as an induction motor,
produces a slip frequency excitation that varies from 120 Hz at starting to 0 Hz at
synchronism. When a synchronous machine pulls out, it will produce a sinusoidal
excitation at the pull out frequency, till it is disconnected or resynchronized. The
critical speed with twice the slip frequency during starting cannot be avoided.

5.10 TORSIONAL ANALYSIS 213
200
400
Torsional
resonant
frequency
(Hz)
600
800
1000
2000
Operating speed r/min
0 4000 6000
1x electrical and mechanical
2nd electrical
4
8
t
h
e
l
e
c
t
r
i
c
a
l
3
6
t
h
e
l
e
c
t
r
i
c
a
l
2
4
t
h
e
l
e
c
t
r
i
c
a
l
1
2
t
h
e
l
e
c
t
r
i
c
a
l
1st
2nd
3rd
4th
5th
6th
7th
8th
9th
10th
11th
12th
Figure 5.29 Torsional interference diagram of a 15000-hp synchronous motor. Source:
Ref. [36].
The critical speed with the slip frequency excitation following pull out can be
avoided, if the machine is de-energized in time.
5.10.2 Excitation from Mechanical System
There can be excitations from the mechanical system too, which are proportional to
speed and may occur at a frequency of multiple of shaft revolution or integral multiple
of gear tooth passing frequency. These are due to imperfections in the mechanical
system and are generally of smaller magnitude. Excitations can also occur from the
load system. A mechanical jam may produce severe dynamic torques.
It may be difficult to totally avoid some amplification of the torques during
stating; however, it should show damping trend as the drive train quickly passes
through the vibration mode. The torsional analysis requires host of motor and load
data, starting characteristics, inertias, and spring constants. These are summarized
in Table 5.4. A torsional analysis may discover many natural frequencies of the
system.
Torsional analysis should also be carried out during starting and short circuit.
Reference [37] illustrates that during starting of a 6000-hp induction motor drive for
a high-speed compressor at 16 000 rpm, it passes through two resonant frequencies.
The motor can even stall during acceleration, and its acceleration time will be higher
as it passes through two low-level torque points during acceleration.

TABLE 5.4 Data Required for Torsional Vibration Analysis
Parameter Description
Mm Maximum transient shaft torque during starting
Ms Breakaway torque refiner
F1 Transferred thrust load to motor at zero end gap in thrust bearings,
both directions
P1 Power loss in the refiner during idling
Critical damping Critical damping in the shaft system in %
Fatigue analysis Data include shaft diameter, speed ratio, material, shear stress, and
stress concentration factor due to step change in shaft diameter
J1, J2, J3, J4 Rotating inertias in kg-m2
of lb ft2
K1, K2, K3 Spring constants, Nm/rad or lb-in/rad
Motor Starting torque–speed characteristics, average and oscillating torques,
effect of variation of system voltage and starting conditions
Load Starting torque–speed characteristics
To illustrate the impact of harmonics on starting a 3000-hp, 4.16-kV,
single-cage induction motor, connected to a step-down transformer is started under
two conditions:
• Normal balanced power supply conditions, devoid of any harmonics.
• The power supply system polluted with seventh harmonic.
Figure 5.30(a) shows normal torque–speed starting curve, while Fig. 5.30(b)
shows starting with supply system polluted with seventh harmonics. This shows that
though the motor is able to start, serious torque oscillations continue to occur due
to harmonic torque. These can be much damaging to the motor shaft. The motor is
started with low inertial load to reduce starting time.
5.10.3 Analysis
An n-spring connected rotating masses can be described by the equations:
J
d𝜔m
dt
+ D𝜔m + H 𝜃m = Tturbine − Tgenerator (5.32)
H is diagonal matrix of stiffness coefficients, 𝜃m is the vector of angular positions, 𝜔m
is the vector of mechanical speeds, Tturbine is the vector of torques applied to turbine
stages, and D is the diagonal matrix of damping coefficients. The moment of inertia
and damping coefficients are available from design data. The spring action creates a
torque proportional to the angle twist.
Figure 5.31(a) shows a torsional system model for the steam turbine generator.
The masses will rotate at one or more of the turbine mechanical natural frequencies
called torsional mode frequencies. When the mechanical system oscillates under such

5.10 TORSIONAL ANALYSIS 215
0 0.5 1 1.5 2 3 4 5
2.5
Time (s)
(a)
(b)
Teg_ASM1@machine@1
Teg_ASM1@machine@1
3.5 4.5
0
−6
−4
−2
0
2
4
Torque
pu
(NM)
6
8
−6
−4
−2
0
2
4
Torque
pu
(NM)
6
0.5 1 1.5 2 3 4 5
2.5
Time (s)
3.5 4.5
Figure 5.30 (a) Simulated normal starting torque–speed characteristics of a 4.16-kV,
3000-hp, single-cage induction motor from balanced supply system; (b) starting
characteristics with supply system polluted with 7th harmonic, EMTP simulations.

T1
J1 J2 J3 J4 J5 J6
T2
K12
HP RH
(a)
(b)
LP1 LP2
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
GEN EXC
K23 K34 K45 K56
T3 T4 T5 T6
Figure 5.31 (a) Rotating mass model of steam turbine generator; (b) oscillation modes.
Source: Ref. [38].
steady state at one or more natural frequencies, the relative amplitude and phase of
individual turbine-rotor elements are fixed and are called mode shapes of torsional
motion, Fig. 5.31(b) [38].
Torsional mode damping quantifies the decay of torsional oscillations. The ratio
of natural log of the successive peaks of oscillation is called logarithmic decrement.
The decrement factor is defined as the time in seconds to decay from the original
point to 1∕e of its value.
The modal spring–mass model is a mathematical representation of Fig. 5.31
for oscillation in mode n given by
|
|
|
|
|
|
|
|
|
|
J1
J2
.
.
Jn
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
̈
𝜃1
̈
𝜃2
̈
𝜃n
|
|
|
|
|
|
|
|
|
|
+
|
|
|
|
|
|
|
|
|
|
K12 −K12
−K12 K12 K23 −K23
−K23 . . −Kn1,n
. .
−Kn1,n Kn1,n
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
𝜃1
𝜃2
.
.
𝜃n
|
|
|
|
|
|
|
|
|
|
=
|
|
|
|
|
|
|
|
|
|
T1
T2
.
.
Tn
|
|
|
|
|
|
|
|
|
|
(5.33)

5.11 SUBSYNCHRONOUS RESONANCE 217
The derivation follows from eigenvectors and frequencies of the spring–mass model.
It is seen that there are n second-order differential equations of motion for an n mass
model and coupled to one another by spring elements.
Diagonalization of the stiffness term would yield n decoupled equations called
the modal spring–mass models. This diagonalization can be accomplished by coor-
dinate transformation from a reference frame in the rotors to a reference frame of the
eigenvectors.
5.11 SUBSYNCHRONOUS RESONANCE
We have defined the SSR in the opening paragraph of this chapter. The exchange
of the energy with a turbine generator takes place at one or more of the natural fre-
quencies of the combined system, and these frequencies are below the synchronous
frequency of the system.
The turbine generator shaft has natural modes of oscillations, which can be at
subsynchronous frequencies. If the induced subsynchronous torque coincides with
one of the shaft natural modes of oscillation, the shaft will oscillate at this natural
frequency, sometimes with high amplitude. This may cause shaft fatigue and possible
failure. The interactions can be caused by
1. Induction generator effect: The resistance of rotor to subsynchronous currents
is negative and network presents a resistance that is positive. If the negative
resistance of the generator is greater than the positive system resistance, there
will be sustained subsynchronous currents.
2. Torsional interaction has been described earlier.
3. Transient torques that result from a system disturbance cause changes in the
network, resulting in sudden changes in the current that will oscillate at the
natural frequency of the network.
The series compensation of the transmission lines is the most common cause
of subsynchronous resonance.
5.11.1 Series Compensation of Transmission Lines
Series compensation of HV transmission lines is used for (1) voltage stability, as it
reduces the series reactive impedance to minimize the receiving end voltage varia-
tions and the possibility of voltage collapse, (2) improvement of transient stability by
increasing the power transmission by maintaining the midpoint voltage during swings
of the machines, and (3) power oscillation damping by varying the applied compensa-
tion so as to counteract the accelerating and DC-accelerating swings of the machines.
A fixed type of series compensation can, however, give rise to subsynchronous oscil-
lations as we will discuss.
An implementation schematic of the series capacitor installation is not shown
here, see Ref. [38].

A series capacitor has a natural resonant frequency given by
fn =
1
2𝜋
√
LC
(5.34)
fn is usually less than the power system frequency. At this frequency, the electrical
system may reinforce one of the frequencies of the mechanical resonance, causing
subsynchronous resonance (SSR). If fr is the subsynchronous resonance frequency
of the compensated line, then at resonance
2𝜋frL =
1
2𝜋frC
fr =f
√
Ksc (5.35)
This shows that the subsynchronous resonance occurs at frequency fr, which is equal
to normal frequency multiplied by the square root of the degree of compensation,
it is typically between 15 and 30 Hz. As the compensation is in 25-75% range, fr
is lower than f. The transient currents at subharmonic frequency are superimposed
upon power frequency component and may be damped out within a few cycles by
the resistance of the line. Under certain conditions, subharmonic currents can have
a destabilizing effect on rotating machines. If the electrical circuit oscillates, then
the subharmonic component of the current results in a corresponding subharmonic
field in the generator. This field rotates backward with respect to the main field and
produces an alternating torque on the rotor at the difference frequency f − fr. If the
mechanical resonance frequency of the shaft of the generator coincides with this
frequency, damage to the generator shaft can occur. A dramatic voltage rise can
occur if the generator quadrature axis reactance and the system capacitive reactance
are in resonance. There is no field winding or voltage regulator to control quadrature
axis flux in a generator. Magnetic circuits of transformers can be driven to saturation
and surge arresters can fail. The inherent dominant subsynchronous frequency
characteristics of the series capacitor can be modified by a parallel-connected
TCR.
If the series capacitor is thyristor or GTO controlled (TCSC), then the whole
operation changes. It can be modulated to damp out any subsynchronous as well
as low-frequency oscillations. Thyristor-controlled series capacitors have been
employed for many HVDC projects.
5.11.2 Subsynchronous Resonance HVDC Systems
Subsynchronous resonance can occur in HVDC systems due to interaction between
oscillations in transmission systems and mechanical torsional vibrations in generator
turbine set. This is mainly brought out by negative damping in HVDC control loop.
By designing HVDC controls with positive damping, the situation can be avoided.
This torsional interaction is significant near the converter substations and is negligible

IREF
IRES
Current
amplifier
Pulse
generator
Pulse
distribution
Current
feedback
To thyristor gates
Aux transformer
Converter transformer
ΔI
Σ
Figure 5.32 Control circuit diagram for HVDC IPC control.
for generators away from the converter stations. The negative damping increases with
increased HVDC power flow and increased delay angle control of the thyristors. The
short-circuit levels in the AC system have an impact - the higher short-circuit levels
have higher damping effects.
The firing angle control system can include a subsynchronous damping con-
troller to secure positive damping. It detects torsional mode of oscillations in rota-
tional velocity of generator by frequency modulation of converter AC voltage. The
torsional-mode oscillations are counteracted by the modulation of converter firing
angles.
The AC- and DC-side harmonics are controlled by having AC and DC filters
(Chapter 15). The harmonic voltages in AC systems are of positive and negative
sequences and have three-phase unbalance. At a harmonic resonance, the harmonic
voltages can be magnified. There are two methods of firing angle controls:
• Individual phase control (IPC)
• Equidistant phase control (EPC)
Individual phase control is not much in use now. The control pulses are derived
from commutation voltage. As discussed in Chapter 4, the start of conduction of indi-
vidual thyristors is delayed with respect to phase angle of zero crossing. The control
circuit diagram is shown in Fig. 5.32. The control function (say VCF) is derived from
the reference current IREF, current margin ΔI, and feedback current IRES (I response).
It is seen that the instant of control pulse and the firing delay angle 𝛼 depends on the
phase voltage derived from the auxiliary transformer and the control function, VCF.
In this method, the distortion in the AC supply waveform can cause variation of firing
angle 𝛼 and lead to instability.
In EPC, the pulses are derived from a pulse generator at a frequency of
6f (six-pulse converter) or 12f (12-pulse converter) where f is the fundamental
frequency. These pulses are separated in a pulse distribution unit and applied to

VC2
VC1
VCF
F1
F1′
1′
d′
d
Δα
Δα
Δα
2′
2 3′
3 4′
4
1
F2′ F3′ F4′
F2 F3 F4
Figure 5.33 Control circuit operation of Fig. 5.32.
0
0 10 20 30 40 50
Frequency (Hz)
60 70 80 90 100
20
40
60
80
Z
bus,
500
kV
100
120
140
160
Figure 5.34 Frequency scan of 500-kV bus at the secondary (500 kV) of the transformer,
EMTP simulation.
individual thyristors. If the power source frequency is considered stable and constant,
the control pulses are equidistant with constant frequency. The pulses are delivered
to converter via a ring counter, which has required number of stages (6 or 12) with
only one stage active at any time. The stages are sequentially switched giving a short
output pulse, one per cycle. For a 12-pulse converter, the pulses are obtained at an
interval of 2𝜋∕12.
Figure 5.33 illustrates that the control function VCF are pulses at a constant
slope, generated at the intersection of the controller voltage VC. These points of inter-
sections are marked F1, F2, … for VC1 and F1′, F2′, … for the voltage VC2. The
distance d or d′ between consecutive control pulses in same and determined by the
slope of the control function VCF. This control function ramp is selected so that pulse
interval is exactly 2πf∕p, where p is the pulse number of converter. If the control
function is increased from VC1 to VC2, the points of intersections are shifted and the
firing angle is increased by Δ𝛼.

−6
0 0.5 1 1.5 2 2.5
Time (s)
3 3.5 4 4.5 5
−5
−4
−3
−2
−1
0
Mass-torque
1
2
3
Figure 5.35 Shaft torque transients, mass 1, EMTP simulation (Example 5.1).
Example 5.1: Consider a 600-MVA, 22-kV generator connected to a step-up
transformer of 600 MVA, delta–wye connected, 22–500 kV, wye windings solidly
grounded, which feeds into a 400-mile-long 500-kV line. A CP model of the
transmission line is modeled in EMTP. A series capacitor compensation of 50%
at the terminal point of the transmission line is provided. For subsynchronous
oscillations, the shaft mass system of steam turbine generators is modeled with
four masses of certain inertia constants connected together through spring constants
(HP and LP sections of turbine, rotor, and exciter). The line serves receiving end
loads. External torques can be applied to each of the masses, for example, turbine,
generator, and exciter masses. An EMTP simulation of the frequency scan at the
500-kV side of the step-up transformer is shown in Fig. 5.34. This shows one
resonance at 19 Hz and the other close to the fundamental frequency. A three-phase
fault occurs at the secondary of the transformer at 1 s and cleared at 1.1 s, fault
duration = 6 cycles. The resulting torque transients in the 500-MVA synchronous
machine mass 1 are shown in Fig. 5.35, with a total simulation time of 5 s. It is seen
that these transients do not decay even after 5 s and diverge, imposing stresses on
the generator shaft and mechanical systems. The angular frequency of mass 1 (zero
external torque that will give maximum swings) is plotted in Fig. 5.36. This shows
violent speed variations. The frequency relays or vibration probes may isolate the
generator from the system. The generator parameters for the EMTP model are as
follows:
Field current at rated voltage = 1200A, Ra = 0.0045, X0 = 0.12, Xd =
1.65, X′
d
= 0.25, X′′
d
= 0.20, X′
q = 0.46, X′′
q = 0.20 all in pu.
T′
qo = 0.55, T′′
qo = 0.09, Tdo = 4.5, T′′
do
= 0.04 all in seconds.
The generator is modeled with AVR and PSS (power system stabilizer). The
transformer is rated 22–500 kV, 600 MVA, %Z = 10% (also see Ref [38]).

−0.95
1
1.05
ω
Omega_1_SM1@machine@1
0 0.5 1 1.5 2 2.5
t
3 3.5 4 4.5 5
Figure 5.36 Angular speed transients, mass 1, with no external torque, EMTP simulation
(Example 5.1).
400A, 10s
!0 MW, 0.85 PF
G
52 52
13.8 kV Bus 1
Source Z+ = 0.0175+j 0.210 pu
(100 MVA base)
5 MVA, Z = 6%
2.4 kV Bus 2
ASD
600 kvar
Fault at 1s, removed in 6 cycles
Load, 7.5 MW, 0.82 PF
Figure 5.37 A circuit configuration for study of subsynchronous oscillation due to an ASD
cascade (Example 5.2).

0.95
0 0.5 1 1.5 2 2.5
t (sec)
3 3.5 4 4.5 5
1
1.05
Omega,
mass
1
1.1
1.15
1.2
1.25
1.3
1.35
Figure 5.38 Angular speed transients, mass 1, EMTP simulation, 10 MW generator
operating alone (Example 5.2).
Torque
(pu)
0 0.5 1 1.5 2 2.5
t
3 3.5 4 4.5 5
Tm_1_SM1@machine@1
Figure 5.39 Shaft torque transients, mass 1, 10-MW generator operating alone, EMTP
simulation (Example 5.2).

The NGH-SSR (after Narain Hingorani Subsynchronous Resonance Sup-
pressor), Ref. [39,40], scheme can minimize subsynchronous electrical torque and
hence mechanical torque and shaft twisting, limit build up of oscillations due to
subsynchronous resonance, and protect series capacitors from overvoltages, not
discussed here.
5.11.3 Subsynchronous Resonance Drive Systems
In Section 5.2.2, the interharmonics due to drive systems are discussed. In this section,
we stated that for inverter frequencies of 25, 37.5, and 48 Hz and source frequency of
60 Hz, the side band pairs are 10 and 110, 15 and 135 Hz, and 36 and 156 Hz, respec-
tively. These can create subsynchronous resonance, though a number of conditions
and parameters must coincide for such an event.
Example 5.2: To illustrate subsynchronous resonance in an ASD, an EMTP sim-
ulation of the simple drive system shown in Fig. 5.37 is carried out. A 10-MVA
generator supplies loads connected to its bus and may operate in synchronism with
utility source. It supplies 12-pulse ASD load connected through a step-down trans-
former of 5 MVA. To compensate the load voltage dip at 2.4-kV bus, a 600-kvar
capacitor bank is provided. Characteristic harmonics of the order of 11th and 13th
are modeled. Also pair of harmonics 36 and 156 are modeled. The turbine generator
0 0.5 1.5
1 2.5
2
t (sec)
3.5
3 4.5
4 5
0 0.5 1.5
1 2.5
2
t
3.5
3 4.5
4 5
0 0.5
Line
current,
phases
a,
b,
c
1.5
1 2.5
2
t
3.5
3 4.5
4 5
Figure 5.40 Transient line currents of 10-MW generator in three phases, EMTP simulation
(Example 5.2).

REFERENCES 225
train is modeled with four rotating masses and spring constants. The disturbance is
modeled as a three-phase fault on 2.4-kV bus at 1 s, cleared in six cycles.
The resonant frequency of the system as calculated on 13.8-kV bus 1 occurs at
45.8 Hz when the load is entirely supplied by the generator. When the generator is
operating in synchronism with the utility, there is only a small shift in the resonant
frequency.
Figures 5.38 and 5.39 illustrate the speed and torque oscillations of mass 1,
respectively. The transients have only decayed slightly over a period of 5 s. When
the generator is operated in synchronism with the utility, the torque oscillations of
mass 1 are slightly lower. Figure 5.40 shows the line current oscillations of the gen-
erator. Ref. [41] provides further reading.
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